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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Hybrid Improved Empirical Mode Decomposition and Artificial Neural Network Model for the Prediction of Critical Heat Flux (CHF)

Three Hybrid artificial neural network (ANN) models namely radial basis function (RBF), generalized regression neural networks (GRNN), and multi-layer perceptron (MLP) combined with empirical mode decomposition (EMD) are developed for CHF predictive modelling using CHF experimental databases.First, the original experimental inputs data series are decomposed into several intrinsic mode functions (IMFs) and one residual by EMD, whose components are divided into high, medium and low components. The performance parameters of the hybrid models indicates that the root mean square error (RMSE) are 0.8831, 0.6522, and 0.4149; the mean absolute error (MAE) are 0.6697, 0.4636, and 0.1935. The values of the R-square of the developed prediction approach utilizing EMD-RBF, EMD-GRNN, and EMD-MLP models are 0.8553, 0.9302, and 0.9818, and the index of agreement are 0.9464, 0.9700, and 0.9894., The value of the R-square and the index of agreement of the proposed models are much higher than those of the simple models .The Pearson's test results show that the association strength between the measured and the predicted values of the proposed model EMD-MLP is the strongest. These results show the following: (a) compared with other related, recent studies, the prediction accuracy of the hybrid model EMD- MLP proposed in this research is the best hybrid model; (b) the proposed hybrid model (EMD-MLP) attains superior performance compared with simple models.

Djeddou, Messaoud↗
DOE OSTI2022

LaplaceInterpolation.jl: A Julia package for fast interpolation on a grid

We implement a linear-time algorithm for interpolation on a regular multidimensional grid in the Julia language. The algorithm is an approximate Laplace interpolation (Press, 1992) when no parameters are given; and when parameters m ∈ Z and ϵ > 0 are set, the interpolant approximates a Matérn kernel, of which radial basis functions and polyharmonic splines are a special case. We implement, in addition, Neumann, Dirichlet (trivial), and average boundary conditions with potentially different aspect ratios in the different dimensions. The interpolant functions in arbitrary dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Distributed fiber sensing systems for 3D combustion temperature field monitoring in coal-fired boilers using optically generated acoustic waves (Final Report)

In this project, we have developed and tested three kinds of fiber optic sensing systems for real time monitoring of temperature variations within an industrial scale boiler furnace. The fiber optic sensing systems target spatial and temporal distributions of high temperature profiles in a boiler furnace in fossil power plants. The reconstructed temperature profile will provide critical input for the control mechanisms to optimize the combustion process. This temperature profile will address the essential problem for fossil power plants in achieving higher efficiency and fewer pollutant emissions. Acoustic pyrometer systems have been used to reconstruct temperature field of power plant boilers based on measuring TOF (times-of-flight) of sound waves along some straight paths in a 2D cross-section of the boiler. In this project, optically generated acoustic signals from a fiber optic sensing system have replaced the acoustic signals generated from an electrical transducer. A 3D reconstruction algorithm replaced the previous 2D model. In this project, three kinds of fiber optic sensing systems have been developed and tested. They are fiber optic sensing system I, fiber optic sensing system II (Distributed Sensing System I) and fiber optic sensing system III (Distributed Sensing System II). For fiber optic sensing system I, the fiber optic ultrasound generator acts as a signal generator. A microphone, hydrophone or other electronic devices serve as a signal receiver. In this system, there are one generator and one receiver. Distance test, water temperature test, air temperature test, air temperature reconstruction, and GE ISBF pilot test were performed by Fiber optic sensing system I. The fiber optic sensing system I successfully detected temperature in all these tests. We got 2D temperature reconstruction results by using the fiber optic sensing system I and it matched the reference data. The fiber optic sensing system I successfully survived in GE ISBF boiler environment (480 °F). For fiber optic sensing system II (Distributed Sensing System I), it is an all optical ultrasound system. The fiber optic ultrasound generator acts as a signal generator. Fiber Bragg Grating (FBG) and Fabry-Perot (FP) sensor act as a signal receiver. In this system, there is one generator and one receiver. Aluminum plate temperature test, furnace high temperature test, and GE ISBF pilot test were performed by the fiber optic sensing system II. Fiber optic sensing system II successfully detected the temperature in all these tests. The fiber optic sensing system II successfully survived at up to 700 °C furnace environment and 320 °C GE ISBF boiler environment. For fiber optic sensing system III (Distributed Sensing System II), it is also an all optical ultrasound system. The fiber optic ultrasound generator acts as a signal generator. Multiple FP fiber sensors act as signal receivers. In this system, there is one generator and three receivers. Three GE ISBF pilot tests were performed by fiber optic sensing system III. The fiber optic sensing system III survived in the cold flow tests in GE’s ISBF pilot test facility. However, we didn’t get high temperature data by using this system since the nanosecond laser issues. During the period of the project, test trials, data simulation and algorithm optimization was performed successfully. For real time temperature field construction, the sampling rate must be fast enough to capture the field variations. The technology of Code-division multiple access (CDMA) is well studied which could allow parallel multiplexing, even if signals overlap in time or frequencies. Moreover, it has been known that extending the length of signal significantly improves SNR. For acoustic signals, these multiplexing techniques have also been widely used, mainly for sonar and acoustic communications. The CDMA modulation technique has been proposed and studied to guarantee high network throughput, low channel access delay and low energy consumption. We have studied the temperature field reconstruction using Gaussian Radial Basis Functions (GRBF)-based approximation approach. Reconstruction of 3D temperature field using Neural Networks with measured TOF and known propagation paths is feasible. 2D and 3D temperature field reconstruction simulation results are achieved. The milestone status is shown in Table 1. We finished milestone 1-8 and milestone 10. For milestone 9, we did three pilot tests by using the fiber optic sensing system III (Distributed Sensing System II) at GE Power. However, due to the failure of the ns laser, we did not get the temperature results. We conducted some additional tasks that were not originally proposed: 1) We fabricated a fiber optic sensing system I and did a pilot test based on this system. 2) In the proposal, we proposed two pilot tests at GE Power. In reality, we finished at least seven pilot tests at GE Power. GE Power has made a lot of efforts for supporting the pilot tests. 3) We got a simulation results based on CDMA. In summary, most of the tasks have been accomplished. The outcome of this project removed a few barriers that hinder the achievement of the final product of the distributed sensing systems. With the successful accomplishment of this project, a prototype of the fiber optic sensing system can be fabricated to attract more interests from companies and other funding agencies.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Sensitivity Analysis of Particle-In-Cell Modeling Parameters in Settling Bed, Bubbling Fluidized Bed and Circulating Fluidized Bed

The objective of the work presented is to perform a preliminary sensitivity analysis of particle-in-cell (PIC) model parameters when applied to settling bed, bubbling fluidized bed, and circulating fluidized bed simulations. These examples correspond to widely different flow conditions commonly seen in chemical engineering applications. Simulations were performed using the PIC method in the open-source software Multiphase Flow with Interphase eXchanges (MFiX) developed by the National Energy Technology Laboratory (NETL). As part of the non-intrusive uncertainty quantification (UQ) analysis, simulation campaigns were generated using Nodeworks. Sampling locations or settings for PIC model parameters were determined using the Latin Hypercube method. Response surfaces were created using radial basis functions (RBF), and Sobol’ indices were estimated to quantify the influence of model parameters on the quantities of interest (QoI). This study marks a first step towards systematically determining optimal ranges for model parameters used in MFiX-PIC. Based on limited experience, it is expected that these values would depend strongly on flow conditions. Given the complexity of the multiphase flow systems under analysis, a non-intrusive UQ based approach is used to identify the most influential parameters in each case. This prior knowledge will help in proposing an effective design of experiments (DoE) and determine optimal parameters through techniques such as deterministic or Bayesian calibration, which will be pursued in the future.

42 ENGINEERING↗
DOE OSTI2024

Reinforcement Learning Control for Enhancing Marine Hydrokinetic Turbine Energy Generation

This paper proposes a reinforcement learning-based method to maximize power generation for a direct-drive marine hydrokinetic turbine. A high levelized cost of energy (LCOE) is preventative in the widespread adoption of many marine energy conversion technologies. A straightforward way to reduce LCOE is to increase conversion efficiency and ensure maximum energy generation. The proposed method utilizes a damping control methodology, varying applied generator torque via a linear relationship between the applied damping coefficient and rotor speed. A state-action-reward-state-action (SARSA) algorithm has been used to learn the optimal control action for a given flow velocity. The proposed SARSA methodology uses Gaussian radial basis functions to create a three-dimensional surface to estimate the relationship between damping coefficient, incoming flow velocity, and coefficient of power (C p ). Here, the SARSA algorithm was compared against a baseline optimal tip speed ratio controller over a year-long flow velocity case profile while considering the effects of biofouling on the turbine system, where the proposed RL method generated 0.92% more energy than the baseline.

Damp↗
DOE OSTI2019

Application and Evaluation of Surrogate Models for Radiation Source Search

Surrogate models are increasingly required for applications in which first-principles simulation models are prohibitively expensive to employ for uncertainty analysis, design, or control. They can also be used to approximate models whose discontinuous derivatives preclude the use of gradient-based optimization or data assimilation algorithms. We consider the problem of inferring the 2D location and intensity of a radiation source in an urban environment using a ray-tracing model based on Boltzmann transport theory. Whereas the code implementing this model is relatively efficient, extension to 3D Monte Carlo transport simulations precludes subsequent Bayesian inference to infer source locations, which typically requires thousands to millions of simulations. Additionally, the resulting likelihood exhibits discontinuous derivatives due to the presence of buildings. To address these issues, we discuss the construction of surrogate models for optimization, Bayesian inference, and uncertainty propagation. Specifically, we consider surrogate models based on Legendre polynomials, multivariate adaptive regression splines, radial basis functions, Gaussian processes, and neural networks. We detail strategies for computing training points and discuss the merits and deficits of each method.

Cook, Jared A.↗
DOE OSTI2021

Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

German, Péter (ORCID:0000000307285283)↗
DOE OSTI2020

Multi-objective optimization of peel and shear strengths in ultrasonic metal welding using machine learning-based response surface methodology

Ultrasonic metal welding (UMW) is a solid-state joining technique with varied industrial applications. Despite of its numerous advantages, UMW has a relative narrow operating window and is sensitive to variations in process conditions. As such, it is imperative to quantitatively characterize the influence of welding parameters on the resulting joint quality. The quantification model can be subsequently used to optimize the parameters. Conventional response surface methodology (RSM) usually employs linear or polynomial models, which may not be able to capture the intricate, nonlinear input-output relationships in UMW. Furthermore, some UMW applications call for simultaneous optimization of multiple quality indices such as peel strength, shear strength, electrical conductivity, and thermal conductivity. To address these challenges, this paper develops a machine learning (ML)-based RSM to model the input-output relationships in UMW and jointly optimize two quality indices, namely, peel and shear strengths. The performance of various ML methods including spline regression, Gaussian process regression (GPR), support vector regression (SVR), and conventional polynomial regression models with different orders is compared. A case study using experimental data shows that GPR with radial basis function (RBF) kernel and SVR with RBF kernel achieve the best prediction accuracy. The obtained response surface models are then used to optimize a compound joint strength indicator that is defined as the average of normalized shear and peel strengths. In addition, the case study reveals different patterns in the response surfaces of shear and peel strengths, which has not been systematically studied in the literature. While developed for the UMW application, the method can be extended to other manufacturing processes.

42 ENGINEERING↗
DOE OSTI2020

Weighted greedy-optimal design of computer experiments for kernel-based and Gaussian process model emulation and calibration

This article is concerned with the approximation of high-dimensional functions by kernel-based methods. Motivated by uncertainty quantification, which often necessitates the construction of approximations that are accurate with respect to a probability density function of random variables, we aim at minimizing the approximation error with respect to a weighted $L^p$-norm. We present a greedy procedure for designing computer experiments based upon a weighted modification of the pivoted Cholesky factorization. The method successively generates nested samples with the goal of minimizing error in regions of high probability. Numerical experiments validate that this new importance sampling strategy is superior to other sampling approaches, especially when used with non-product probability density functions. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Multivariate Space‐Time Dynamic Model for Characterizing the Atmospheric Impacts Following the Mt. Pinatubo Eruption

The June 1991 Mt. Pinatubo eruption resulted in a massive increase of sulfate aerosols in the atmosphere, absorbing radiation and leading to global changes in surface and stratospheric temperatures. A volcanic eruption of this magnitude serves as a natural analog for stratospheric aerosol injection, a proposed solar radiation modification method to combat a warming climate. The impacts of such an event are multifaceted and region-specific. Our goal is to characterize the multivariate and dynamic nature of the atmospheric impacts following the Mt. Pinatubo eruption. We developed a multivariate space-time dynamic linear model to understand the full extent of the spatially- and temporally-varying impacts. Specifically, spatial variation is modeled using a flexible set of basis functions for which the basis coefficients are allowed to vary in time through a vector autoregressive (VAR) structure. This novel model is cast in a Dynamic Linear Model (DLM) framework and estimated via a customized MCMC approach. We demonstrate how the model quantifies the relationships between key atmospheric parameters prior to and following the Mt. Pinatubo eruption with reanalysis data from MERRA-2 and highlight when such a model is advantageous over univariate models.

Dynamic Linear Model↗
DOE OSTI2025

Kernel Manifolds: Nonlinear‐Augmentation Dimensionality Reduction Using Reproducing Kernel Hilbert Spaces

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. In conclusion, we compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.

kernel methods↗
DOE OSTI2021

Cholesky-based experimental design for Gaussian process and kernel-based emulation and calibration.

Gaussian processes and other kernel-based methods are used extensively to construct approximations of multivariate data sets. The accuracy of these approximations is dependent on the data used. This paper presents a computationally efficient algorithm to greedily select training samples that minimize the weighted L p error of kernel-based approximations for a given number of data. The method successively generates nested samples, with the goal of minimizing the error in high probability regions of densities specified by users. The algorithm presented is extremely simple and can be implemented using existing pivoted Cholesky factorization methods. Training samples are generated in batches which allows training data to be evaluated (labeled) in parallel. For smooth kernels, the algorithm performs comparably with the greedy integrated variance design but has significantly lower complexity. Numerical experiments demonstrate the efficacy of the approach for bounded, unbounded, multi-modal and non-tensor product densities. We also show how to use the proposed algorithm to efficiently generate surrogates for inferring unknown model parameters from data using Bayesian inference.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Guidelines for creating artificial neural network empirical interatomic potential from first-principles molecular dynamics data under specific conditions and its application to $α$-Ag 2 Se

First-principles molecular dynamics (FPMD) simulations are highly accurate, but due to their high calculation cost, the computational scale is often limited to hundreds of atoms and few picoseconds under specific temperature and pressure conditions. As such, we present here the guidelines for creating artificial neural network empirical interatomic potential (ANN potential) trained with such a limited FPMD data, which can perform long time scale MD simulations at least under the same conditions. The FPMD data for training are prepared on the basis of the convergence of radial distribution function [$g(r)$]. While training the ANN using total energy and atomic forces of the FPMD data, the error of pressure is also monitored and minimized. To create further robust potential, we add a small amount of FPMD data to reproduce the interaction between two atoms that are close to each other. ANN potentials for $α$-Ag 2 Se were created as an application example, and it has been confirmed that not only $g(r)$ and mean square displacements but also the specific heat requiring a long time scale simulation matched the FPMD and the experimental values. In addition, the MD simulation using the ANN potential achieved over 10 4 acceleration over the FPMD one. The guidelines proposed here mitigate the creation difficulty of the ANN potential, and a lot of FPMD data sleeping on the hard disk after the research may be put on the front stage again.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

PyFLOSIC: Python-based Fermi–Löwdin orbital self-interaction correction

We present pyflosic, an open-source, general-purpose python implementation of the Fermi–Löwdin orbital self-interaction correction (FLO-SIC), which is based on the python simulation of chemistry framework (pyscf) electronic structure and quantum chemistry code. Thanks to pyscf, pyflosic can be used with any kind of Gaussian-type basis set, various kinds of radial and angular quadrature grids, and all exchange-correlation functionals within the local density approximation, generalized-gradient approximation (GGA), and meta-GGA provided in the libxc and xcfun libraries. A central aspect of FLO-SIC is the Fermi-orbital descriptors, which are used to estimate the self-interaction correction. Importantly, they can be initialized automatically within pyflosic; they can also be optimized within pyflosic with an interface to the atomic simulation environment, a python library that provides a variety of powerful gradient-based algorithms for geometry optimization. Although pyflosic has already facilitated applications of FLO-SIC to chemical studies, it offers an excellent starting point for further developments in FLO-SIC approaches, thanks to its use of a high-level programming language and pronounced modularity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Scattering phase shifts and mixing angles for an arbitrary number of coupled channels on the lattice

We present a lattice method for determining scattering phase shifts and mixing angles for the case of an arbitrary number of coupled channels. Previous nuclear lattice effective field theory simulations were restricted to mixing of up to two partial waves for scattering of two spin-1/2 particles, which is insufficient for analyzing nucleon-nucleus or nucleus-nucleus scattering processes. In the proposed method, the phase shifts and mixing angles are extracted from the radial wave functions obtained by projecting the three-dimensional lattice Hamiltonian onto the partial wave basis. In this work, we use a spherical wall potential as a boundary condition along with a channel-mixing auxiliary potential to construct the full-rank S matrix. Our method can be applied to particles with any spin, but we focus here on scattering of two spin-1 bosons involving up to four coupled channels. For a considered test potential, the phase shifts and mixing angles extracted on the lattice are shown to agree with the ones calculated by solving the Schrödinger equation in the continuum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Extending the SAGA Survey (xSAGA). I. Satellite Radial Profiles as a Function of Host-galaxy Properties

We present "Extending the Satellites Around Galactic Analogs Survey" (xSAGA), a method for identifying low-z galaxies on the basis of optical imaging and results on the spatial distributions of xSAGA satellites around host galaxies. Using spectroscopic redshift catalogs from the SAGA Survey as a training data set, we have optimized a convolutional neural network (CNN) to identify z < 0.03 galaxies from more-distant objects using image cutouts from the DESI Legacy Imaging Surveys. From the sample of >100,000 CNN-selected low-z galaxies, we identify >20,000 probable satellites located between 36–300 projected kpc from NASA-Sloan Atlas central galaxies in the stellar-mass range $9.5\lt \mathrm{log}({M}_{\star }/{M}_{\odot })\lt 11$. We characterize the incompleteness and contamination for CNN-selected samples and apply corrections in order to estimate the true number of satellites as a function of projected radial distance from their hosts. Satellite richness depends strongly on host stellar mass, such that more-massive host galaxies have more satellites, and on host morphology, such that elliptical hosts have more satellites than disky hosts with comparable stellar masses. We also find a strong inverse correlation between satellite richness and the magnitude gap between a host and its brightest satellite. The normalized satellite radial distribution between 36–300 kpc does not depend on host stellar mass, morphology, or magnitude gap. The satellite abundances and radial distributions we measure are in reasonable agreement with predictions from hydrodynamic simulations. Our results deliver unprecedented statistical power for studying satellite galaxy populations and highlight the promise of using machine-learning for extending galaxy samples of wide-area surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Theory and application of the vector pair correlation function for real-space crystallographic analysis of order/disorder correlations from STEM images

Deviations of local structure and chemistry from the average crystalline unit cell are increasingly recognized to have a significant influence on the properties of many technologically important materials. Here, we present the vector pair correlation function (vPCF) as a new real-space crystallographic analysis method, which can be applied to atomic-resolution scanning transmission electron microscopy (STEM) images to quantify and analyze structural order/disorder correlations. Our STEM-based vPCFs have several advantages over radial PCFs and/or 3D pair distribution functions from x-ray total scattering: vPCFs explicitly retain crystallographic orientation information, are spatially resolved, can be applied directly on a sublattice basis, and are suitable for any material that can be imaged with STEM. To show the utility of our approach, we measure partial vPCFs in Ba 5 SmSn 3 Nb 7 O 30 (BSSN), a tetragonal tungsten bronze (TTB) structured complex oxide. Many TTBs are known to be classical or relaxor ferroelectrics, and these properties have been correlated with the presence of superlattice ordering. BSSN, specifically, exhibits relaxor behavior and an incommensurate structural modulation. From the vPCF data, we observe that, of the cation sites, only the Ba (A2) sublattice is structurally modulated. We then infer the local modulation vector and reveal a marked anisotropy in its correlation length. Finally, short-range correlated polar displacements on the B2 cation sites are observed. This work introduces the vPCF as a powerful real-space crystallography technique, which enables direct, robust quantification of short-to-long range order on a sublattice-specific basis and is applicable to a wide range of complex material types.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

In many recent applications, particularly in the field of atom-centered descriptors for interatomic potentials, tensor products of spherical harmonics have been used to characterize complex atomic environments. When coupled with a radial basis, the atomic cluster expansion (ACE) basis is obtained. However, symmetrization with respect to both rotation and permutation results in an overcomplete set of ACE descriptors with linear dependencies occurring within blocks of functions corresponding to particular generalized Wigner symbols. All practical applications of ACE employ semi-numerical constructions to generate a complete, fully independent basis. While computationally tractable, the resultant basis cannot be expressed analytically, is susceptible to numerical instability, and thus has limited reproducibility. Here we present a procedure for generating explicit analytic expressions for a complete and independent set of ACE descriptors. The procedure uses a coupling scheme that is maximally symmetric w.r.t. permutation of the atoms, exposing the permutational symmetries of the generalized Wigner symbols, and yields a permutation-adapted rotationally and permutationally invariant basis (PA-RPI ACE). Theoretical support for the approach is presented, as well as numerical evidence of completeness and independence. A summary of explicit enumeration of PA-RPI functions up to rank 6 and polynomial degree 32 is provided. The PA-RPI blocks corresponding to particular generalized Wigner symbols may be either larger or smaller than the corresponding blocks in the simpler rotationally invariant basis. Finally, we demonstrate that basis functions of high polynomial degree persist under strong regularization, indicating the importance of not restricting the maximum degree of basis functions in ACE models a priori.

74 ATOMIC AND MOLECULAR PHYSICS↗